OCR A-Level Product Design mathematical and technical principles: a complete overview

What this topic demands

This topic is the applied mathematics that runs through Component 01. Every other technical area (materials, manufacture, structures, mechanisms, electronics, sustainability) sets calculation questions, and this topic gathers the formulae and methods. The reward is choosing the right formula, substituting in consistent units, stating the unit of the answer, and interpreting the result. Marks are lost on unit slips and inverted formulae, and gained by clear, complete working. This overview ties the four dot-point pages together.

Stress, strain and Young's modulus

Stress is force over area ($\sigma = \frac{F}{A}$, pascals); strain is extension over original length ($\varepsilon = \frac{\Delta L}{L}$, no units); Young's modulus is stress over strain ($E = \frac{\sigma}{\varepsilon}$, pascals or gigapascals) and measures stiffness. Convert lengths to metres and areas to square metres, and remember stiffness is not strength. See stress, strain and Young's modulus.

Costing and quantities

Calculate quantities from areas and volumes, percentage waste as $\frac{\text{waste}}{\text{total}} \times 100$, and cost as materials plus labour plus overheads, then add a mark-up (a percentage of cost) to get the selling price. Use the radius in circle areas and apply the mark-up to the total cost, not just the materials. See costing and quantities.

Scale, ratio and tolerance

At a scale of $1:n$, actual = drawing $\times n$ and drawing = actual $\div n$. Split a quantity by ratio by finding one part (total over the sum of the ratio numbers) then multiplying out. A tolerance gives upper and lower limits and a band (their difference). Check the scale direction and keep units consistent. See scale, ratio and tolerance maths.

Electrical and mechanical calculations

Power is $P = VI$ (watts); energy is power times time (kWh for kilowatts times hours); Ohm's law is $V = IR$. Mechanical advantage is load over effort; velocity ratio is effort distance over load distance; efficiency is $\frac{\text{MA}}{\text{VR}} \times 100$ percent, always below 100 because of friction and moving-part weight. A moment is force times perpendicular distance. The skill is choosing the right formula. See electrical and mechanical calculations.

How to revise this topic

1. Memorise the formulae. Stress, strain, Young's modulus, waste, cost, mark-up, scale, ratio, tolerance, power, energy, Ohm's law, MA, VR, efficiency, moments.
2. Convert units first. Lengths to metres, areas to square metres, watts to kilowatts, minutes to hours.
3. Keep strain unitless. And always state the unit of every other answer.
4. Choose the right formula. Identify what is given and what is asked.
5. Interpret and sense-check. Compare results with known values, then attempt the quiz.